International System of Units
The International System of Units (abbreviated SI from ) is the modern form of the metric system and is the world's most widely used system of measurement, used in both everyday commerce and science. It comprises a coherent system of units of measurement built around seven base units, 22 named and an indeterminate number of unnamed coherent derived units, and a set of prefixes that act as decimal-based multipliers. It is primarily called "Standards International". The standards, published in 1960 as the result of an initiative started in 1948, are based on the metre–kilogram–second (MKS) system, rather than the centimetre–gram–second (CGS) system, which, in turn, had several variants. The SI has been declared to be an evolving system; thus prefixes and units are created and unit definitions are modified through international agreement as the technology of measurement progresses, and as the precision of measurements improves. The driving force behind the development of the Système international was the diversity of units that had sprung up within the CGS system of units and the lack of coordination between the various disciplines that made extensive use of units of measurement. In addition to defining a new realisation of the metric system, the General Conference on Weights and Measures, an organisation set up by the Convention of the Metre in 1875, succeeded in bringing together many international organizations to agree not only the definitions of the SI, but also rules on writing and presenting measurements in a standardised manner around the globe. The system has been adopted by most countries in the developed (OECD) world, though within English-speaking countries, the adoption has not been universal. In the United States metric units are not commonly used outside of science, medicine and the government; however, United States customary units are officially defined in terms of SI units. The United Kingdom has officially adopted a partial metrication policy, with no intention of replacing imperial units entirely. Canada has adopted it for most governmental and scientific purposes, but imperial units are still legally permitted and remain in common use throughout many sectors of Canadian society, particularly in the buildings, trades and railways sectors. History /Italian border at Pontebba displaying myriametres, a unit of 10 km used in Central Europe in the 19th century (but since deprecated). ]] The metric system was first implemented during the French Revolution (1790s) with just the metre and kilogram as standards of length and massThe differences between "weight" and "mass" were only formally qualified in 1901. respectively. In the 1830s Carl Friedrich Gauss laid the foundations for a coherent system based on length, mass and time. In the 1860s a group working under the auspices of the British Association for the Advancement of Science formulated the requirement for a coherent system of units with base units and derived units. The inclusion of electrical units into the system was hampered by the customary use of more than one set of units, until 1900 when Giovanni Giorgi identified the need to define one single electrical quantity as a fourth base quantity alongside the original three base quantities. Meanwhile, in 1875, the Treaty of the Metre passed responsibility for verification of the kilogram and metre against agreed prototypes from French to international control. In 1921 the Treaty was extended to include all physical quantities including electrical units originally defined in 1893. In 1948 an overhaul of the metric system was set in motion which resulted in the development of the "Practical system of units" which, on its publication in 1960, was given the name "The International System of Units". In 1954 the 10th General Conference on Weights and Measures (CGPM) identified electric current as the fourth base quantity in the practical system of units and added two more base quantities—temperature and luminous intensity—making six base quantities in all. The units associated with these quantities were the metre, kilogram, second, ampere, degree Kelvin and candela. In 1971 a seventh base quantity, amount of substance represented by the mole, was added to the definition of SI. Uncoordinated development The metric system was developed from 1791 onwards by a committee of the Académie des sciences commissioned by the Assemblée nationale and Louis XVI of France to create a unified and rational system of measures. The group, which included Antoine-Laurent Lavoisier (the "father of modern chemistry") and the mathematicians Pierre-Simon Laplace and Adrien-Marie Legendre, used the principles for relating length, volume and mass that had been proposed by the English cleric John Wilkins in 1668 ; and the concept of using the earth's meridian as the basis of the definition of length, originally proposed in 1670 by the French cleric Gabriel Mouton. On 30 March 1791, the Assemblée adopted the principles proposed by the committee for the new decimal system of measure and authorized a survey between Dunkirk and Barcelona to establish the length of the meridian. On 11 July 1792, the committee proposed the names "metre", "are", "litre" and "grave" for the units of length, area, capacity and mass respectively. The committee also proposed that multiples and submultiples of these units were to be denoted by decimal-based prefixes such as "centi-" to denote "one hundredth" and "kilo-" to denote "one thousand". The law of 7 April 1795 ( ) defined the terms gramme and kilogramme, which replaced the former terms gravet (correctly milligrave) and grave, and on 22 June 1799, after Pierre Méchain and Jean-Baptiste Delambre completed the meridian survey, the definitive standards, the mètre des Archives and the kilogramme des Archives were deposited in the ''Archives nationales''. On 10 December 1799 (a month after Napoleon's coup d'état), the law by which the metric system was to be definitively adopted in France ( ) was passed. During the first half of the nineteenth century there was little consistency in the choice of preferred multiples of the base units – typically the myriametre ( metres) was in widespread use in both France and parts of Germany, while the kilogram (1000 grams) rather than the myriagram was used for mass. In 1832 Carl Friedrich Gauss, assisted by Wilhelm Weber, implicitly defined the second as a base unit when he quoted the earth's magnetic field in terms of millimetres, grams, and seconds. Prior to this, the strength of the earth’s magnetic field had only been described in relative terms. The technique used by Gauss was to equate the torque induced on a suspended magnet of known mass by the earth’s magnetic field with the torque induced on an equivalent system under gravity. The resultant calculations enabled him to assign dimensions based on mass, length and time to the magnetic field. In the 1860s James Clerk Maxwell, William Thomson (later Lord Kelvin) and others working under the auspices of the British Association for the Advancement of Science, built on Gauss' work and formalised the concept of a coherent system of units with base units and derived units. The principle of coherence was successfully used to define a number of units of measure based on the centimetre–gram–second (CGS) system of units (CGS), including the erg for energy, the dyne for force, the barye for pressure, the poise for dynamic viscosity and the stokes for kinematic viscosity. Metre Convention |} A French-inspired initiative for international cooperation in metrology led to the signing in 1875 of the Metre Convention. Initially the convention only covered standards for the metre and the kilogram. A set of 30 prototypes of the metre and 40 prototypes of the kilogram,The text "Des comparaisons périodiques des étalons nationaux avec les prototypes internationaux" ( ) in article 6.3 of the Metre Convention distinguishes between the words "standard" (OED: "The legal magnitude of a unit of measure or weight") and "prototype" (OED: "an original on which something is modelled"). in each case made of a 90% platinum-10% iridium alloy, were manufactured by the British firm Johnson, Matthey & Co and accepted by the CGPM in 1889. One of each was selected at random to become the International prototype metre and International prototype kilogram that replaced the mètre des Archives and kilogramme des Archives respectively. Each member state was entitled to one of each of the remaining prototypes to serve as the national prototype for that country. }} The treaty established three international organisations to oversee the keeping of international standards of measurement: * General Conference on Weights and Measures (Conférence générale des poids et mesures or CGPM) – a meeting every four to six years of delegates from all member states that receives and discusses a report from the CIPM and that endorses new developments in the SI on the advice of the CIPM. * International Committee for Weights and Measures (Comité international des poids et mesures or CIPM) – a committee that meets annually at the BIPM and is made up of eighteen individuals of high scientific standing, nominated by the CGPM to advise the CGPM on administrative and technical matters * International Bureau of Weights and Measures (Bureau international des poids et mesures or BIPM) – an international metrology centre at Sèvres in France that has custody of the International prototype kilogram, provides metrology services for the CGPM and CIPM, houses the secretariat for these organisations and hosts their formal meetings. Initially its prime metrological purpose was a periodic recalibration of national prototype metres and kilograms against the international prototype. In 1921 the Metre Convention was extended to include all physical units, including the ampere and others defined by the Fourth International Conference of Electricians in Chicago in 1893, thereby enabling the CGPM to address inconsistencies in the way that the metric system had been used. The official language of the Metre Convention is French and the definitive version of all official documents published by or on behalf of the CGPM is the French-language version. Towards SI , Liberia and Burma.]] At the close of the 19th century three different systems of units of measure existed for electrical measurements: a CGS-based system for electrostatic units (also known as the Gaussian or ESU system), a CGS-based system for electromechanical units (EMU) and an MKS-based system (the "International system") for electrical distribution systems. Attempts to resolve the electrical units in terms of length, mass and time using dimensional analysis was beset with difficulties—the dimensions depended on whether one used the ESU or EMU systems. This anomaly was resolved in 1900 when Giovanni Giorgi published a paper in which he advocated using a fourth base unit alongside the existing three base units. The fourth unit could be chosen to be either electric current or voltage or electrical resistance. In the late 19th and early 20th centuries a number of non-coherent units of measure based on the gram/kilogram, the centimetre/metre and the second, such as the Pferdestärke (metric horsepower) for power, Pferd is German for "horse" and stärke is German for "strength" or "power". The Pferdestärke is the power needed to raise 75 kg against gravity at the rate of one metre per second. ( ). the darcy for permeability and the use of "millimetres of mercury" for the measurement of both barometric and blood pressure were developed or propagated. All these units incorporate standard gravity in their definitions. At the end of the Second World War, a number of different systems of measurement were in use throughout the world. Some of these systems were metric system variations, whereas others were based on customary systems of measure. After representations by the International Union of Pure and Applied Physics (IUPAP) and by the French Government, the 9th General Conference on Weights and Measures (CGPM), in 1948, asked the International Committee for Weights and Measures (CIPM) to conduct an international study of the measurement needs of the scientific, technical, and educational communities and "to make recommendations for a single practical system of units of measurement, suitable for adoption by all countries adhering to the Metre Convention".9th CGPM (1948): Resolution 6 On the basis of the findings of this study, the 10th CGPM in 1954 decided that an international system should be derived from six base units to provide for the measurement of temperature and optical radiation in addition to mechanical and electromagnetic quantities. Six base units were recommended: the metre, kilogram, second, ampere, degree Kelvin (later renamed kelvin), and candela. In 1960, the 11th CGPM named the system the International System of Units, abbreviated SI from the French name, . 11th CGPM (1960): Resolution 12 The BIPM has also described SI as "the modern metric system". The seventh base unit, the mole, was added in 1971 by the 14th CGPM.14th CGPM (1971):Resolution 3 SI Brochure and conversion factors The CGPM have published a brochure, the 8th edition of which appeared in 2006, in which the various recommendations that make up SI have been codified. The official version of the brochure, in line with the provisions of the Metre Convention, is the French version. This brochure leaves some scope for local interpretation, particularly in respect of language. The United States National Institute of Standards and Technology has produced a version of the CGPM document (NIST SP 330) which clarifies local interpretation for English-language publications that use American English and another document (NIST SP 811) that gives general guidance for the use of SI in the United States. The writing and maintenance of the CGPM brochure is carried out by one of the consultative committees of the International Committee for Weights and Measures (CIPM): the Consultative Committee for Units (CCU). The CIPM nominates the chairman of this committee, and the committee includes representatives of various other international bodies rather than CIPM or CGPM nominees. These bodies include: *International Organization for Standardization (ISO) *National Institute of Standards and Technology (NIST) (United States) *National Physical Laboratory (NPL) (British) *International Astronomical Union (IAU) *International Union of Pure and Applied Chemistry (IUPAC) *International Union of Pure and Applied Physics (IUPAP) *International Commission on Illumination (CIE) ( ) *Committee on Data for Science and Technology (CODATA) – an interdisciplinary committee of the International Council for Science. *International Commission on Radiation Units and Measurements (ICRU) *International Federation of Clinical Chemistry and Laboratory Medicine (IFCC) *International Electrotechnical Commission (IEC) *International Organization of Legal Metrology (OIML) ( ) *National Institute of Advanced Industrial Science and Technology (AIST) (Japan) *National Institute for Natural and Engineering Sciences (PTB) (Germany) ( ) *Federal Agency on Technical Regulating and Metrology This committee also provides a forum for the bodies concerned to provide input to the CIPM in respect of ongoing enhancements to SI. In 2010 the CCU proposed a number of changes to the definitions of the base units used in SI. The CIPM meeting of October 2010 found that the proposal was not complete, and it is expected that the CGPM will consider the full proposal in 2014. The definitions of the terms "quantity", "unit", "dimension" etc. that are used in the SI Brochure are those given in the International Vocabulary of Metrology, a publication produced by the Joint Committee for Guides in Metrology (JCGM), a working group consisting of eight international standards organisations under the chairmanship of the director of the BIPM. The quantities and equations that define the SI units are now referred to as the International System of Quantities (ISQ), and are set out in the ISO/IEC 80000 Quantities and Units. Appendix B of NIST SP 811, a list of conversion factors between SI and customary units, is an extension to the SI Brochure. Units and prefixes The International System of Units consists of a set of base units, a set of derived units with special names, and a set of decimal-based multipliers that are used as prefixes. The term "SI Units" includes all three categories, but the term "coherent SI units" includes only base units and coherent derived units. Base units Base units are the building blocks of SI – all other units of measure can be derived from the base units. When Maxwell first introduced the concept of a coherent system, he identified three quantities that could be used as base units – mass, length and time. Giorgi later identified the need for an electrical base unit – theoretically electrical current, potential difference, electrical resistance, electrical charge or any one of a number of other units could have been used as the base unit, with the remaining units being then defined by the laws of physics – the unit of electric current was chosen for SI. The remaining three base units were added later. Derived units Derived units are formed by powers, products or quotients of the base units and are unlimited in number; Derived units are associated with derived quantities, for example velocity is a quantity that is derived from the base quantities of time and distance which, in SI, has the dimensions metres per second (symbol m/s). The dimensions of derived units can be expressed in terms of the dimensions of the base units. Coherent units are derived units that contain no numerical factor other than 1—quantities such as standard gravity and density of water are absent from their definitions. In the example above, one newton is the force required to accelerate a mass of one kilogram by one metre per second squared. Since the SI units of mass and acceleration are kg and m⋅s−2 respectively and , the units of force (and hence of newtons) is formed by multiplication to give kg⋅m⋅s−2. Since the newton is part of a coherent set of units, the constant of proportionality is 1. For the sake of convenience, some derived units have special names and symbols. Such units may themselves be used in combination with the names and symbols for base units and for other derived units to express the units of other derived quantities. For example, the SI unit of force is the newton (N), the SI unit of pressure is the pascal (Pa)—and the pascal can be defined as "newtons per square metre" (N/m2). Prefixes Prefixes are added to unit names to produce multiple and sub-multiples of the original unit. All multiples are integer powers of ten, and above a hundred or below a hundredth all are integer powers of a thousand. For example, kilo-'' denotes a multiple of a thousand and ''milli-'' denotes a multiple of a thousandth; hence there are one thousand millimetres to the metre and one thousand metres to the kilometre. The prefixes are never combined, and multiples of the kilogram are named as if the gram were the base unit. Thus a millionth of a metre is a ''micrometre, not a millimillimetre, and a millionth of a kilogram is a milligram, not a microkilogram. Non-SI units accepted for use with SI Although, in theory, SI can be used for any physical measurement, the CIPM has recognised that some non-SI units still appear in the scientific, technical and commercial literature, and will continue to be used for many years to come. In addition, certain other units are so deeply embedded in the history and culture of the human race that they will continue to be used for the foreseeable future. They have catalogued a number of such non-SI units accepted for use with SI and published them in the SI Brochure, thereby ensuring that their use is consistent across the globe. These units have been grouped as follows: This grouping and the reference to Tables 6, 7, 8 and 9 reflects the 8th Edition of the SI Brochure (2006) *'Non-SI units accepted for use with the SI' (Table 6): :Certain units of time, angles and legacy non-SI metric units have a long history of consistent use. Most of mankind has used the day and its non-decimal subdivisions as a basis of time and, unlike the foot or the pound, these were the same regardless of where they were being measured. The radian, being of a revolution, has mathematical niceties, but it is cumbersome for navigation, and, as with time, the units used in navigation have a large degree of consistency around the world. The tonne, litre and hectare were adopted by the CGPM in 1879 and have been retained as units that may be used alongside SI units, having been given unique symbols. The catalogued units are ::minute, hour, day, degree of arc, minute of arc, second of arc, hectare, litre and tonne * Non-SI units whose values in SI units must be obtained experimentally (Table 7). :Physicists often use units of measure that are based on natural phenomena, particularly when the quantities associated with these phenomena are many orders of magnitude greater than or less than the equivalent SI unit. The most common ones have been catalogued in the SI Brochure together with consistent symbols and accepted values, but with the caveat that their physical values need to be measured.The CGPM have defined the metre in terms of the speed of light, so the speed of light has an exact value. ::electronvolt, dalton/unified atomic mass unit, astronomical unit, Planck constant and electron mass * Other non-SI units (Table 8): :A number of non-SI units that had never been formally sanctioned by the CGPM have continued to be used across the globe in many spheres including health care and navigation. As with the units of measure in Tables 6 and 7, these have been catalogued by the CIPM in the SI Brochure to ensure consistent usage, but with the recommendation that authors who use them should define them wherever they are used. ::bar, millimetre of mercury, ångström, nautical mile, barn, knot, neper and [[decibel]] * Non-SI units associated with the CGS and the CGS-Gaussian system of units (Table 9) :The SI manual also catalogues a number of legacy units of measure that are used in specific fields such as geodesy and geophysics or are found in the literature, particularly in classical and relativistic electrodynamics where they have certain advantages: The units that are catalogued are: ::erg, dyne, poise, stokes, stilb, phot, gal, maxwell, gauss and œrsted. Writing unit symbols and the values of quantities Before 1948, the writing of metric quantities was haphazard. In 1879, the CIPM published recommendations for writing the symbols for length, area, volume and mass, but it was outside its domain to publish recommendations for other quantities. Beginning in about 1900, physicists who had been using the symbol "μ" for "micrometre" (or "micron"), "λ" for "microlitre", and "γ" for "microgram" started to use the symbols "μm", "μL" and "μg", but it was only in 1935, a decade after the revision of the Metre Convention that the CIPM formally adopted this proposal and recommended that the symbol "μ" be used universally as a prefix for . In 1948, the ninth CGPM approved the first formal recommendation for the writing of symbols in the metric system when the basis of the rules as they are now known was laid down. These rules were subsequently extended by International Organization for Standardization (ISO) and the International Electrotechnical Commission (IEC) and now cover unit symbols and names, prefix symbols and names, how quantity symbols should be written and used and how the values of quantities should be expressed. Both ISO and the IEC have published rules for the presentation of SI units that are generally compatible with those published in the SI Brochure. ISO and IEC were in the process of merging their standards for quantities and units into a single set of compatible documents identified as the ISO/IEC 80000 Standard. The rules covering printing of quantities and units are part of ISO 80000-1:2009. Unit names Names of units follow the grammatical rules associated with common nouns: in English and in French they start with a lowercase letter (e.g., newton, hertz, pascal), even when the symbol for the unit begins with a capital letter. This also applies to "degrees Celsius", since "degree" is the unit. In German, however, the names of units, as with all German nouns, start with capital letters. The spelling of unit names is a matter for the guardiansFor example, the Académie française in the case of French or Council for German Orthography ( ) in the case of German of the language concerned – the official British and American spellings for certain SI units differ – British English uses the spelling deca-'', ''metre, and litre whereas American English uses the spelling deka-'', ''meter, and liter, respectively. Likewise, the plural forms of units follow the grammar of the language concerned: in English, the normal rules of English grammar are used, e.g. "henries" is the plural of "henry". However, the units lux, hertz, and siemens have irregular plurals in that they remain the same in both their singular and plural form. In English, when unit names are combined to denote multiplication of the units concerned, they are separated with a hyphen or a space (e.g. newton-metre or newton metre). The plural is formed by converting the last unit name to the plural form (e.g. ten newton-metres). Chinese and Japanese expressway distances road sign in eastern Beijing. Although the primary text is in Chinese, the distances use the internationally recognised numerals and symbols.]] Chinese uses traditional logograms for writing the unit names, while in Japanese unit names are written in the phonetic katakana script; in both cases symbols are written using the internationally recognised Latin and Greek characters. ;Japanese A set of characters representing various metric units was created in Japan in the late 19th century. Characters exist for three base units: the metre ( ), litre ( ) and gram ( ). These were combined with a set of six prefix characters – kilo-'' ( ), ''hecto-'' ( ), ''deca-'' ( ), ''deci-'' ( ), ''centi-'' ( ) and ''milli-'' ( ) – to form an additional 18 single-character units. The seven length units (kilometre to millimetre), for example, are and . These characters, however, are not in common use today; instead, units are written out in katakana, the Japanese syllabary used for foreign borrowings, such as '' for "kilometer". A few Sino-Japanese words for these units remain in use in Japanese, most significantly "square meter", but otherwise borrowed pronunciations are used. These characters are examples of the rare phenomenon of single-character loan words – a foreign word represented by a single Japanese character – and form the plurality of such words. Similar characters were also coined for other units, such as British units, though these also have fallen out of use; see Single character gairaigo: Metric units and Single character gairaigo: Other units for a full list. ;Chinese The basic units are metre ( ), litre ( ), gram ( ), and second ( ), while others include watt ( ). Prefixes include deci-'' ( '' ), centi-'' ( '' ), milli-'' ( '' ), micro-'' ( '' ), and kilo-'' ( '' ). These are combined to form disyllabic characters, such as 'centimeter' or 'kilowatt'. In the 19th century various compound characters were also used, similar to Japanese, either imported or formed on the same principles, such as for (kilowatt) or for . These are generally not used today – for example centimetres is usually written – but are occasionally found in older or technical writing.Victor Mair, "Polysyllabic characters in Chinese writing", Language Log, 2011 August 2 Unit symbols and the values of quantities Although the writing of unit names is language-specific, the writing of unit symbols and the values of quantities is consistent across all languages and therefore the SI Brochure has specific rules in respect of writing them. The guideline produced by the National Institute of Standards and Technology (NIST) clarifies language-specific areas in respect of American English that were left open by the SI Brochure, but is otherwise identical to the SI Brochure. General rules General rulesExcept where specifically noted, these rules are common to both the SI Brochure and the NIST brochure. for writing SI units and quantities apply to text that is either handwritten or produced using an automated process: * The value of a quantity is written as a number followed by a space (representing a multiplication sign) and a unit symbol; e.g., 2.21 kg, , 22 K. This rule explicitly includes the percent sign (%) and the symbol for degrees of temperature (°C). Exceptions are the symbols for plane angular degrees, minutes, and seconds (°, ′, and ″), which are placed immediately after the number with no intervening space. * Symbols are mathematical entities, not abbreviations, and as such do not have an appended period/full stop (.), unless the rules of grammar demand one for another reason, such as denoting the end of a sentence. * A prefix is part of the unit, and its symbol is prepended to the unit symbol without a separator (e.g., k in km, M in MPa, G in GHz). Compound prefixes are not allowed. * Symbols for derived units formed by multiplication are joined with a centre dot (·) or a non-breaking space; e.g., N·m or N m. * Symbols for derived units formed by division are joined with a solidus (/), or given as a negative exponent. E.g., the "metre per second" can be written m/s, m s−1, m·s−1, or . Only one solidus should be used; e.g., kg/(m·s2) and kg·m−1·s−2 are acceptable, but kg/m/s2 is ambiguous and unacceptable. * The first letter of symbols for units derived from the name of a person is written in upper case; otherwise, they are written in lower case. E.g., the unit of pressure is named after Blaise Pascal, so its symbol is written "Pa", but the symbol for mole is written "mol". Thus, "T" is the symbol for tesla, a measure of magnetic field strength, and "t" the symbol for tonne, a measure of mass. Since 1979, the litre may exceptionally be written using either an uppercase "L" or a lowercase "l", a decision prompted by the similarity of the lowercase letter "l" to the numeral "1", especially with certain typefaces or English-style handwriting. The American NIST recommends that within the United States "L" be used rather than "l". * Symbols of units do not have a plural form; e.g., 25 kg, not 25 . * Uppercase and lowercase prefixes are not interchangeable. E.g., the quantities 1 mW and 1 MW represent two different quantities; the former is the typical power requirement of a hearing aid (1 milliwatt or 0.001 watts), and the latter the typical power requirement of a suburban train (1 megawatt or watts). * The 10th resolution of CGPM in 2003 declared that "the symbol for the decimal marker shall be either the point on the line or the comma on the line." In practice, the decimal point is used in English-speaking countries and most of Asia, and the comma in most of Latin America and in continental European languages. * Spaces should be used as a thousands separator ( ) in contrast to commas or periods (1,000,000 or 1.000.000) to reduce confusion resulting from the variation between these forms in different countries. * Any line-break inside a number, inside a compound unit, or between number and unit should be avoided. Where this is not possible, line breaks should coincide with thousands separators. * Since the value of "billion" and "trillion" can vary from language to language, the dimensionless terms "ppb" (parts per billion) and "ppt" (parts per trillion) should be avoided. However, no alternative is suggested in the SI Brochure. Printing SI symbols Further rules are specified in respect of production of text using printing presses, word processors, typewriters and the like. * Symbols are written in upright (Roman) type (m for metres, s for seconds), so as to differentiate from the italic type used for quantities (m'' for mass, ''s for displacement). By consensus of international standards bodies, this rule is applied independent of the font used for surrounding text. * In Chinese, Japanese, and Korean language computing (CJK), some of the commonly used units, prefix–unit combinations, or unit–exponent combinations have been allocated predefined single characters taking up a full square. Unicode includes these in its CJK Compatibility and letter-like symbols sub-ranges for back compatibility, without necessarily recommending future usage. These are summarised in Unicode symbols. The cursive ℓ, a letter-like symbol, has been used in a number of countries in addition to China and Japan as a symbol for the litre, but this is not currently recommended by any standards body. *In print, the space used as a thousands separator (commonly called a thin space) is typically narrower than that used between words. Realisation of units used for measuring the Avogadro constant to a relative uncertainty of 2 or less. ]] Metrologists carefully distinguish between the definition of a unit and its realisation. The definition of each base unit of the SI is drawn up so that it is unique and provides a sound theoretical basis on which the most accurate and reproducible measurements can be made. The realisation of the definition of a unit is the procedure by which the definition may be used to establish the value and associated uncertainty of a quantity of the same kind as the unit. A description of the mise en pratique''This term is a translation of the official French text of the SI Brochure of the base units is given in an electronic appendix to the SI Brochure. The published ''mise en pratique is not the only way in which a base unit can be determined: the SI Brochure states that "any method consistent with the laws of physics could be used to realise any SI unit." In the current (2012) exercise to overhaul the definitions of the base units, various consultative committees of the CIPM have required that more than one mise en pratique shall be developed for determining the value of each unit. In particular: * At least three separate experiments be carried out yielding values having a relative standard uncertainty in the determination of the kilogram of no more than and at least one of these values should be better than . Both the Watt balance and the Avogadro project should be included in the experiments and any differences between these be reconciled. *When the kelvin is being determined, the relative uncertainty of the Boltzmann constant derived from two fundamentally different methods such as acoustic gas thermometry and dielectric constant gas thermometry be better than one part in and that these values be corroborated by other measurements. Post-1960 changes The preamble to the Metre Convention read "Desiring the international uniformity and precision in standards of weight and measure, have resolved to conclude a convention ...". Changing technology has led to an evolution of the definitions and standards that has followed two principal strands – changes to SI itself and clarification of how to use units of measure that are not part of SI, but are still nevertheless used on a worldwide basis. Changes to the SI Since 1960 the CGPM has made a number of changes to SI. These include: *The 13th CGPM (1967) renamed the "degree Kelvin" (symbol °K) to the "kelvin" (symbol K) *The 14th CGPM (1971) added the mole (symbol mol) to the list of base units.pg 221 – McGreevy *The 14th GCPM (1971) added the pascal (symbol Pa) for pressure and the siemens (symbol S) for electrical conductance to the list of named derived units. *The 15th CGPM (1975) added the becquerel (symbol Bq) for "activity referred to a radionuclide" and the gray (symbol Gy) for ionizing radiation to the list of named derived units *In order to distinguish between "absorbed dose" and "dose equivalent", the 16th CGPM (1979) added the sievert (symbol Sv) to the list of named derived units as the unit of dose equivalent. *The 16th CGPM (1979) clarified that in a break with convention either the letter "L" or the letter "l" may be used as a symbol for the litre. – the traditional device that measures blood pressure using mercury in a manometer. Pressures are recorded in "millimetres of mercury" – a non-SI unit]] *The 21st CGPM (1999) added the katal (symbol kat) for catalytic activity to the list of named derived units. *In its original form (1960), the SI defined prefixes for values ranging from pico- (symbol p) having a value of 10−12 to tera- (symbol T) having a value of 1012. The list was extended at the 12th CGPM (1964), at the 15th CGPM (1975) and at the 19th CGPM (1991) to give the current range of prefixes. In addition, advantage was taken of developments in technology to redefine many of the base units enabling the use of higher precision techniques. Retention of non-SI units Although, in theory, SI can be used for any physical measurement, it is recognised that some non-SI units still appear in the scientific, technical and commercial literature, and will continue to be used for many years to come. In addition, certain other units are so deeply embedded in the history and culture of the human race that they will continue to be used for the foreseeable future. The CIPM has catalogued such units and included them in the SI Brochure so that they can be used consistently. The first such group comprises the units of time and of angles and certain legacy non-SI metric units. Most of mankind has used the day and its subdivisions as a basis of time with the result that the second, minute, hour and day, unlike the foot or the pound, were the same regardless of where it was being measured. The second has been catalogued as an SI unit, its multiples as units of measure that may be used alongside the SI. The measurement of angles has likewise had a long history of consistent use – the radian, being of a revolution, has mathematical niceties, but it is cumbersome for navigation, hence the retention of the degree, minute and second of arc. The tonne, litre and hectare were adopted by the CGPM in 1879 and have been retained as units that may be used alongside SI units, having been given unique symbols. Physicists often use units of measure that are based on natural phenomena such as the speed of light, the mass of a proton (approximately one dalton), the charge of an electron and the like. These too have been catalogued in the SI Brochure with consistent symbols, but with the caveat that their physical values need to be measured.The CGPM has defined the metre in terms of the speed of light, so the speed of light has an exact value. In the interests of standardising health-related units of measure used in the nuclear industry, the 12th CGPM (1964) accepted the continued use of the curie (symbol Ci) as a non-SI unit of activity for radionuclides; the becquerel, sievert and gray were adopted in later years. Similarly, the millimetre of mercury (symbol mmHg) was retained for measuring blood pressure. "New SI" s (in grey) with fixed numerical values in the proposed system. Unlike the current (2013) definition, the base units are derived from one or more constants of nature.]] When the metre was redefined in 1960, the kilogram was the only SI base unit that relied on a specific artifact and thus the only unit that was subject to "periodic comparisons of national standards with the international prototypes". After the 1996–1998 recalibration, a clear divergence between the various prototype kilograms was observed. At its 23rd meeting (2007), the CGPM mandated the CIPM to investigate the use of natural constants of nature as the basis for all units of measure rather than the artefacts that were then in use, thus involving a change from explicit unit definitions to explicit constant definitions. At a meeting of the CCU held in Reading, United Kingdom, in September 2010, a resolution and draft changes to the SI Brochure that were to be presented to the next meeting of the CIPM in October 2010 were agreed to in principle. The proposals that the CCU put forward were: *In addition to the speed of light, four constants of nature – the Planck constant, an elementary charge, the Boltzmann constant and the Avogadro number – be defined to have exact values. *The International prototype kilogram be retired *The current definitions of the kilogram, ampere, kelvin and mole be revised. *The wording of the definitions of all the base units be both tightened up and changed to reflect the change in emphasis from explicit unity to explicit constant definitions. The CIPM meeting of October 2010 found that "the conditions set by the General Conference at its 23rd meeting have not yet been fully met. For this reason the CIPM does not propose a revision of the SI at the present time". The CIPM did however sponsor a resolution at the 24th CGPM in which the changes were agreed to in principle and which were expected to be finalised at the CGPM's next meeting in 2014. See also Notes References Further reading * * Unit Systems in Electromagnetism * [http://www.nist.gov/customcf/get_pdf.cfm?pub_id=32943 MW Keller et al.] Metrology Triangle Using a Watt Balance, a Calculable Capacitor, and a Single-Electron Tunneling Device * "The Current SI Seen From the Perspective of the Proposed New SI". Barry N. Taylor. Journal of Research of the National Institute of Standards and Technology, Vol. 116, No. 6, Pgs. 797–807, Nov–Dec 2011. External links ;Official * BIPM Bureau International des Poids et Mesures (SI maintenance agency) (home page) ** BIPM brochure (SI reference) * [http://www.iso.org/iso/iso_catalogue/catalogue_ics/catalogue_detail_ics.htm?csnumber=30669 ISO 80000-1:2009 Quantities and units – Part 1: General] * NIST Official Publications ** NIST Special Publication 330, 2008 Edition: The International System of Units (SI) ** NIST Special Publication 811, 2008 Edition: Guide for the Use of the International System of Units ** NIST Special Pub 814: Interpretation of the SI for the United States and Federal Government Metric Conversion Policy * Rules for SAE Use of SI (Metric) Units * * EngNet Metric Conversion Chart Online Categorised Metric Conversion Calculator * U.S. Metric Association. 2008. A Practical Guide to the International System of Units ;History * LaTeX SIunits package manual gives a historical background to the SI system. ;Research * [http://www.npl.co.uk/server.php?show=ConWebDoc.1835 The metrological triangle] * Recommendation of ICWM 1 (CI-2005) ;Pro-metric advocacy groups * The UK Metric Association * The US Metric Association ;Pro-customary measures pressure groups * Category:International System of Units Category:Systems of units Category:International standards